中文摘要：

在板料成形优化设计等领域中，许多复杂工程优化问题往往表现出高维以及多重非线性耦合性等特征，从而导致此类问题优化收敛效率大幅下降。本文提出了一种基于高斯过程近似模型的高维全局优化方法，此方法最大优势在于：能够建立基于高斯过程近似模型的搜索机制，利用该机制并结合EI（Expected Improvement）准则，对萤火虫算法生成的搜索训练样本进行筛选，从而自动产生新的样本点。在此模式下进行优化迭代能够确保算法的搜索快速集中在全局最优点的较小区域内，进而大幅提升优化效率的同时确保收敛的稳健性。复杂的高维非线性测试函数表明，算法具有处理复杂高维工程问题的能力。此外，算法成功应用于NUMISHEET2013 BENCHMARK2中盒形件的板料成形中，对基于时变的压边力进行了优化设计。同主流的EGO（Efficient Global Optimization）相比，其精度和效率都得到了明显的提升。

英文摘要：

Many complicated optimization problems in sheet forming optimization have characteristics such as high-dimensional and multiple nonlinearly coupling resulting in low optimize convergence efficiency. Therefore, a high-dimensional global optimization method was proposed based on the approximate mode of Gaussian process. The most remarkable advantage of this method was that it could build a search mechanism based on the approximate mode of Gaussian process, and screen the search training samples generated by firefly algorithm to automatically generate new sample points through combining this mechanism with expected improvement criterion. Based on this iterations mode, the search could quickly focus on a small promising area, thus a fast and robust convergence of optimization process could be realized. Tests on complex high-dimensional and nonlinear functions show that the proposed method is capable of dealing with complex high-dimensional engineering problems. Furthermore, the sheet forming process for a rectangular box in NUMISHEET2013 BENCH- MARK2 has been successfully optimized by firefly algorithm. Compared with the popular EGO, the efficiency and accuracy are improved.